The quantum estimation theory is the mathematical framework for approaching the optimization problem of a quantum measurement. It applies to situations where we need to predict the value of a parameter by performing a repeated series of measurements on identical preparations of the system and then processing the data to estimate the value of the unknown parameter [1]}. To achieve all these tasks, we would need quantum phenomena as resources, such as quantum entanglement [2]}, [3]}, quantum discord [4]}, [5]} and quantum coherence [6]}, [7]}, to improve the sensitivity of a system. At the same time, quantum systems place intrinsic restrictions on the sensitivity that can be achieved, for example through Heisenberg uncertainty relations, which state that complementary variables cannot be measured simultaneously with unlimited precision. To determine how quantum properties enhance but also restrict the sensitivity of the system, we model its dynamics and focus on a key quantity which is the quantum Fisher information.
